Ratios & Rates. What is a ratio? A ratio is the comparison between two quantities Have we studied anything that would be considered a ratio? Fractions.

Ratios & Ratios & RatesRates

Ratios & RatesRatios & Rates

What is a ratio?

A ratio is the comparison between two quantities

Have we studied anything that would be considered a ratio?

Fractions are ratios. Fractions compare two quantities.

That's why numbers that can be written in fraction formare called rational numbers


What do ratios look like?

A ratio can be written in the following forms…

2

3

FractionFraction "to""to"

2 to 3

ColonColon

2 : 32 out of 3

"out of""out of"


What is a rate?

A rate is a ratio that compares quantities ofdifferent types of measure.

What are different types of measure?

Different types of measure are measuresthat measure different types of things.


Examples of Different Types of Measures

feet and minutes are different types of measures.

ft measures a distance or length

min measures time

How many feet are in a minute?How many minutes are in a foot?

We can't answer these questions, the units are not the same type of measurement.


Examples of the Same Type of Measurement

gallons and quarts are the same type of measurement.

gal measure a liquid capacity

qt measure a liquid capacity

How many gallons in a quart?How many qt in a gal?

We can answer these questions, the units can be converted to each other.

Though, its probably easiest to convert quarts to gallons.


Are the following pairs of units thesame type or different types?

ft & mi

$ & cents

gal & mi

$ & h

cm & m in & lb

yd & sAbbreviation

Key

ft: feetyd: yardmi: milein: inch

cm: centimeterm: meter

gal: gallonlb: poundh: hour

min: minutes: second$: dollar

The circled pairs are the same type of units.


What do rates look like?

A rate can be written in the following forms…

$2

3lb

FractionFraction "per""per"

$2 per 3lb


Which are rates, which are just ratios?

$2

3lb

$2

30cents

12days

100s

8girls

9boys

19mi

gal

$15

2h

The circled pairs are the rates.


Simplifying Ratios & Rates

Many times we need to simplify ratios and rates.

How do you simplify a ratio?

Since a ratio can be written as a fraction,and since we reduce to simplify a fraction,

we will also reduce in order to simplify a ratio.


Simplifying RatiosSimplifying Ratios

1. Write the ratio as a fraction

2. Reduce

$2

$30

$1 1

$15 15or




2. Reduce

12 :18boys girls

2 : 3boys girls




2. Reduce

Sometimes, we make sure the units are the same!

2 to 90hours minutes

1 : 45hour minutes60 : 45minutes minutes4 : 3minutes minutes


Simplifying Ratios & RatesSimplifying Ratios & Rates

How do you simplify a rate?

Since a rate is a ratio, you can simplify a rateas it was a ratio – reduce.


Simplifying RatesSimplifying Rates

1. Write the rate as a fraction

2. Reduce

$36

15 h

$12

5 h


Simplifying Ratios & RatesSimplifying Ratios & Rates

How do you simplify a rate?

Since a rate is a ratio, you can simplify a rateas it was a ratio – reduce.

A rate can also be simplified by writing it as a unit rate.


What is a unit rate?What is a unit rate?

A unit rate is a rate that is written in terms of 1 unit.

A unit rate is a rate whose denominator is 1 unit.

The following are unit rates…

$12

1 h

65

1

m

s

$1.20

lb

21 /mi gal

70mph


How do you write a rate as a unit rate?How do you write a rate as a unit rate?

Writing a unit rate is quite simple.

Remember, a fraction is a division problem.

To get 1 in the denominator, we simply divide.

Divide the numerator by the denominator.


Writing a unit rateWriting a unit rate


2. Divide numerator by denominator

$12

5 h

$2.4

1 h

2.45 12.0





250

30

mi

gal

8.3mi

gal

8.330 250.0





$12.25

25 oz

$0.49 / oz

0.4925 12.25

Ratios & Rates. What is a ratio? A ratio is the comparison between two quantities Have we studied anything that would be considered a ratio? Fractions.

Documents

unit rates

different types of things

type of units

fraction form

following pairs of units

type of measurement

following formsfraction

measures time